What hypotheses do "nonparametric" two-group tests actually test?

Abstract

In this article, I discuss measures of effect size for two-group comparisons where data are not appropriately analyzed by least-squares methods. The Mann-Whitney test calculates a statistic that is a very useful measure of effect size, particularly suited to situations in which differences are measured on scales that either are ordinal or use arbitrary scale units. Both the difference in medians and the median difference between groups are also useful measures of effect size. © 2012 StataCorp LP.